Anomalous transport and relaxation in classical one-dimensional models

TL;DR

This paper investigates anomalous energy transport in one-dimensional classical models by simulating chains of noisy anharmonic oscillators with conserved quantities, revealing power-law divergence of heat conductivity and supporting a two-universality-classes hypothesis.

Contribution

It introduces a method using conservative noise to efficiently estimate heat conductivity divergence and compares results with theoretical predictions to validate universality classes.

Findings

Heat conductivity diverges as L^alpha with alpha near 1/3 for asymmetric potentials.

Alpha is approximately 0.4 for symmetric potentials.

Finite-size and finite-time effects are effectively controlled in the simulations.

Abstract

After reviewing the main features of anomalous energy transport in 1D systems, we report simulations performed with chains of noisy anharmonic oscillators. The stochastic terms are added in such a way to conserve total energy and momentum, thus keeping the basic hydrodynamic features of these models. The addition of this "conservative noise" allows to obtain a more efficient estimate of the power-law divergence of heat conductivity kappa(L) ~ L^alpha in the limit of small noise and large system size L. By comparing the numerical results with rigorous predictions obtained for the harmonic chain, we show how finite--size and --time effects can be effectively controlled. For low noise amplitudes, the alpha values are close to 1/3 for asymmetric potentials and to 0.4 for symmetric ones. These results support the previously conjectured two-universality-classes scenario.